//
//---------------------  1D  ---------------------
//
//
// Quick is not defined for 1D
//

//
//---------------------  2D  ---------------------
//
//       Staggered Mesh for u-vel and v-vel
//
//   0       1       2       3       4       5   
//
//5      >       >       >       >       > 
//       |       |       |       |       |              
//   ^---+---^---+---^---+---^---+---^---+---^  4       Mesh for scalar fields
//       |       |       |       |       | 
//4      >   o   >   o   >   o   >   o   >               5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  3           +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//3      >   o   >   o   >   o   >   o   >                  +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//   ^---+---^---+---^---+---^---+---^---+---^  2           +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//2      >   o   >   o   >   o   >   o   >               0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//   ^---+---^---+---^---+---^---+---^---+---^  1           0 1   2   3   4 5 
//       |       |       |       |       |                 
//1      >   o   >   o   >   o   >   o   >                 o central node
//       |       |       |       |       |                 x boundary node
//   ^---+---^---+---^---+---^---+---^---+---^  0          > u velocity 
//       |       |       |       |       |                 ^ v velocity
//0      >       >       >       >       >    
//       0       1       2       3       4             
//
//                                                  
//          Volumes for v-velocity
//
//       0       1       2       3       4       
//
//       >       >       >       >       >      5
//       :       :       :       :       :              
//4  ^...+---^---+---^---+---^---+---^---+...^          Mesh for scalar fields
//       |       |       |       |       | 
//       >---o--->---o--->---o--->---o--->      4        5  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |               4  x o | o | o | o x
//3  ^...+...^...+...^...+...^...+...^...+...^              +---+---+---+---+
//       |       |       |       |       |               3  x o | o | o | o x
//       >---o--->---o--->---o--->---o--->      3           +---+---+---+---+
//       |       |       |       |       |               2  x o | o | o | o x
//2  ^...+...^...+...^...+...^...+...^...+...^              +---+---+---+---+
//       |       |       |       |       |               1  x o | o | o | o x
//       >---o--->---o--->---o--->---o--->      2        0  x-x-+-x-+-x-+-x-x
//       |       |       |       |       |                  
//1  ^...+...^...+...^...+...^...+...^...+...^              0 1   2   3   4 5 
//       |       |       |       |       |                 
//       >---o--->---o--->---o--->---o--->      1          o central node
//       |       |       |       |       |                 x boundary node
//0  ^...+---^---+---^---+---^---+---^---+...^             > u velocity 
//       :       :       :       :       :                 ^ v velocity
//       >       >       >       >       >      0
//
//   0       1       2       3       4       5             
//
//                       
//                  |           |           |           |
//                -->-----o----->-----o----->-----o----->-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |  (i,j+1)  |     :     |
//                  |     ^     |    v_N    |     ^     |   
//                  |     :     |     :     |     :     |
//                  |     :     |     :     |     :     |
//                -->-----o---- 3 -- v_n -- 4 ----o----->--  4 = u(i  , j+1)
//                  |     :     |     :     |     :     |    3 = u(i-1, j+1)
//                  |     :     |     :     |     :     |    2 = u(i  , j  )
//                  |    v_W   u_w   v_P   u_e   v_E    |    1 = u(i-1, j  )
//                  |  (i-1,j)  |   (i,j)   |  (i+1,j)  |
//                  |     :     |     :     |     :     |
//                -->-----o---- 1 -- v_s -- 2 ----o----->-- 
//                  |     :     |     :     |     :     |               
//                  |     :     |     :     |     :     |
//                  |     ^     |    v_S    |     ^     |   
//                  |     :     |  (i,j-1)  |     :     |
//                  |     :     |     :     |     :     |
//                -->-----o----->-----o----->-----o----->--
//                  |           |           |           | 
//                  
//               1           3                       2         4 
//   u_w = ( u(i-1,j) + u(i-1,j+1) ) / 2   u_e = ( u(i,j) + u(i,j+1) ) / 2
//   v_n = ( v(i,j) + v(i,j+1) ) / 2     v_s = ( v(i,j) + v(i,j-1) ) / 2
//               

namespace Tuna {

template<class T_number, int Dim>
inline bool Quick_YHay<T_number, Dim>::calcCoefficients2D() 
{
    prec_t dy_dx = Gamma * dy / dx;
    prec_t dx_dy = Gamma * dx / dy;
    prec_t dxy_dt = dx * dy / dt;
    prec_t RaGaVol = Rayleigh * Gamma * 0.5 * dx * dy;
    prec_t ce, cem, cep, cw, cwm, cwp, CE, CW;
    prec_t cn, cnm, cnp, cs, csm, csp, CN, CS;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int i =  bi; i <= ei; ++i)
      for (int j = bj; j <= ej; ++j)
	{
	  CE = ce = ( u(i  ,j) + u(i  ,j+1) ) * 0.5 * dy;
	  CW = cw = ( u(i-1,j) + u(i-1,j+1) ) * 0.5 * dy;
	  CN = cn = ( v(i  ,j) + v(i  ,j+1) ) * 0.5 * dx;
	  CS = cs = ( v(i  ,j) + v(i  ,j-1) ) * 0.5 * dx;
	  cem = cep = 0.0;
	  cwm = cwp = 0.0;
	  cnm = cnp = 0.0;
	  csm = csp = 0.0;

	  // QUICK as presented in Hayase et al. J. of Comput. Phys., 98, 108-118, 1992.
// ---- X 
	  if ( ce > 0 ) { 
	    CE = 0;
	    if (i == bi) {
	      cep = ce * (phi_0(i+1,j) - phi_0(i-1,j)) / 3.0;
	    } else {
	      cep = ce * 0.125 * (-phi_0(i-1,j) - 2*phi_0(i,j) + 3*phi_0(i+1,j));
	    }
	  } else {
	  // The case i == ei is taken in to account in applyBoundaryConditions2D.
	    if (i == ei-1) {
	      cem = ce * (phi_0(i+2,j) - phi_0(i,j)) / 3.0;
	    } else if (i < ei-1){
	      cem = ce * 0.125 * (-phi_0(i+2,j) - 2*phi_0(i+1,j) + 3*phi_0(i,j));
	    }
	  }
	  
	  if ( cw > 0 ) {
 	  // The case i == bi is taken in to account in applyBoundaryConditions2D.
	    if (i == bi+1) {
	      cwp = cw * (phi_0(i,j) - phi_0(i-2,j)) / 3.0;
	    } else if (i > bi+1) {
	      cwp = cw * 0.125 * (-phi_0(i-2,j) - 2*phi_0(i-1,j) + 3*phi_0(i,j));
	    }
	  } else {
	    CW = 0;
	    if (i == ei) {
	      cwm = cw * (phi_0(i-1,j) - phi_0(i+1,j)) / 3.0;
	    } else {
	      cwm = cw * 0.125 * (-phi_0(i+1,j) - 2*phi_0(i,j) + 3*phi_0(i-1,j));
	    }
	  }

 // ---- Y 
	  if ( cn > 0 ) { 
	    CN = 0;
	    cnp = cn * 0.125 * (-phi_0(i,j-1) - 2*phi_0(i,j) + 3*phi_0(i,j+1));
	  } else {
	    if (j == ej) {
	      cnm = cn * 0.125 * (-5*phi_0(i,j+1) + 6*phi_0(i,j) - phi_0(i,j-1));
	    } else {
	      cnm = cn * 0.125 * (-phi_0(i,j+2) - 2*phi_0(i,j+1) + 3*phi_0(i,j));
	    }
	  }
	  
	  if ( cs > 0 ) { 
	    if (j == bj) {
	      csp = cs * 0.125 * (-5*phi_0(i,j-1) + 6*phi_0(i,j) - phi_0(i,j+1));
	    } else {
	      csp = cs * 0.125 * (-phi_0(i,j-2) - 2*phi_0(i,j-1) + 3*phi_0(i,j));
	    }
	  } else {
	    CS = 0;
	    csm = cs * 0.125 * (-phi_0(i,j+1) - 2*phi_0(i,j) + 3*phi_0(i,j-1));
	  }

	  aE (i,j) = dy_dx - CE;
	  aW (i,j) = dy_dx + CW;
	  aN (i,j) = dx_dy - CN;
	  aS (i,j) = dx_dy + CS;
	  aP (i,j) = aE (i,j) + aW (i,j) + aN (i,j) + aS (i,j) + dxy_dt 
	    + (ce - cw) + (cn - cs);

	  sp (i,j) = v(i,j) * dxy_dt - ( p(i,j+1) - p(i,j) ) * dx +
	    RaGaVol * ( T(i,j) + T(i,j+1) )
	    - (cep + cem - cwp - cwm + cnp + cnm - csp - csm);	    	   
	}   
    calc_dv_2D();
    applyBoundaryConditions2D();
    return 0;     
}

//
//---------------------  3D  ---------------------
//
template<class T_number, int Dim>
inline bool Quick_YHay<T_number, Dim>::calcCoefficients3D() 
{
    prec_t dyz = dy * dz, dyz_dx = Gamma * dyz / dx;
    prec_t dxz = dx * dz, dxz_dy = Gamma * dxz / dy;
    prec_t dxy = dx * dy, dxy_dz = Gamma * dxy / dz;
    prec_t dxyz_dt = dx * dy * dz / dt;
    prec_t RaGaVol = Rayleigh * Gamma * 0.5 * dx * dy * dz;
    prec_t ce, cem, cep, cw, cwm, cwp, CE, CW;
    prec_t cn, cnm, cnp, cs, csm, csp, CN, CS;
    prec_t cf, cfm, cfp, cb, cbm, cbp, CF, CB;
    aE = 0.0; aW = 0.0; aN = 0.0; aS = 0.0; aF = 0.0; aB = 0.0; aP = 0.0; 
    sp = 0.0;

    for (int k = bk; k <= ek; ++k)
      for (int i =  bi; i <= ei; ++i)
	for (int j = bj; j <= ej; ++j)
	  {
	    CE = ce = ( u(i  ,j,k) + u(i  ,j+1,k  ) ) * 0.5 * dyz;
	    CW = cw = ( u(i-1,j,k) + u(i-1,j+1,k  ) ) * 0.5 * dyz;
	    CN = cn = ( v(i  ,j,k) + v(i  ,j+1,k  ) ) * 0.5 * dxz;
	    CS = cs = ( v(i  ,j,k) + v(i  ,j-1,k  ) ) * 0.5 * dxz;
	    CF = cf = ( w(i  ,j,k) + w(i  ,j+1,k  ) ) * 0.5 * dxy;
	    CB = cb = ( w(i,j,k-1) + w(i  ,j+1,k-1) ) * 0.5 * dxy;

	    //	    CF = cf = ( w(i  ,j,k) + w(i  ,j  ,k+1) ) * 0.5 * dxy;
	    //	    CB = cb = ( w(i-1,j,k) + w(i-1,j  ,k+1) ) * 0.5 * dxy;

	    cem = cep = 0.0;
	    cwm = cwp = 0.0;
	    cnm = cnp = 0.0;
	    csm = csp = 0.0;
	    cfm = cfp = 0.0;
	    cbm = cbp = 0.0;

	    // QUICK as presented in Hayase et al.
// ---- X
	    if ( ce > 0 ) { 
	      CE = 0;
	      if (i == bi) {
		cep = ce * (phi_0(i+1,j,k) - phi_0(i-1,j,k)) / 3.0;
	      } else {
		cep = ce * 0.125 * (-phi_0(i-1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i+1,j,k));
	      }
	    } else {
	      // The case i == ei is taken in to account in applyBoundaryConditions3D.
	      if (i == ei-1) {
		cem = ce * (phi_0(i+2,j,k) - phi_0(i,j,k)) / 3.0;
	      } else if (i < ei-1) {
		cem = ce * 0.125 * (-phi_0(i+2,j,k) - 2*phi_0(i+1,j,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cw > 0 ) { 
	      // The case i == bi is taken in to account in applyBoundaryConditions3D.
	      if (i == bi+1) {
		cwp = cw * (phi_0(i,j,k) - phi_0(i-2,j,k)) / 3.0;
	      } else if (i > bi+1) {
		cwp = cw * 0.125 * (-phi_0(i-2,j,k) - 2*phi_0(i-1,j,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CW = 0;
	      if (i == ei) {
		cwm = cw * (phi_0(i-1,j,k) - phi_0(i+1,j,k)) / 3.0;
	      } else {
		cwm = cw * 0.125 * (-phi_0(i+1,j,k) - 2*phi_0(i,j,k) + 3*phi_0(i-1,j,k));
	      }
	    }

// ---- Y
	    if ( cn > 0 ) { 
	      CN = 0;
	      cnp = cn * 0.125 * (-phi_0(i,j-1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j+1,k));
	    } else {
	      if (j == ej) {
		cnm = cn * 0.125 * (-5*phi_0(i,j+1,k) + 6*phi_0(i,j,k) - phi_0(i,j-1,k));
	      } else {
		cnm = cn * 0.125 * (-phi_0(i,j+2,k) - 2*phi_0(i,j+1,k) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cs > 0 ) { 
	      if (j == bj) {
		csp = cs * 0.125 * (-5*phi_0(i,j-1,k) + 6*phi_0(i,j,k) - phi_0(i,j+1,k));
	      } else  {
		csp = cs * 0.125 * (-phi_0(i,j-2,k) - 2*phi_0(i,j-1,k) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CS = 0;
	      csm = cs * 0.125 * (-phi_0(i,j+1,k) - 2*phi_0(i,j,k) + 3*phi_0(i,j-1,k));
	    }

// ---- Z
	    if ( cf > 0 ) { 
	      CF = 0;
	      if (k == bk) {
		cfp = cf * (phi_0(i,j,k+1) - phi_0(i,j,k-1)) / 3.0;
	      } else {
		cfp = cf * 0.125 * (-phi_0(i,j,k-1) - 2*phi_0(i,j,k) + 3*phi_0(i,j,k+1));
	      }
	    } else {
	      if (k == ek-1) {
		cfm = cf * (phi_0(i,j,k+2) - phi_0(i,j,k)) / 3.0;
	      } else if (k < ek-1) {
		cfm = cf * 0.125 * (-phi_0(i,j,k+2) - 2*phi_0(i,j,k+1) + 3*phi_0(i,j,k));
	      }
	    }
	    
	    if ( cb > 0 ) { 
	      if (k == bk+1) {
		cbp = cb * (phi_0(i,j,k) - phi_0(i,j,k-2)) / 3.0;
	      } else if (i > bk+1) {
		cbp = cb * 0.125 * (-phi_0(i,j,k-2) - 2*phi_0(i,j,k-1) + 3*phi_0(i,j,k));
	      }
	    } else {
	      CB = 0;
	      if (k == ek) {
		cbm = cb * (phi_0(i,j,k-1) - phi_0(i,j,k+1)) / 3.0;
	      } else {
		cbm = cb * 0.125 * (-phi_0(i,j,k+1) - 2*phi_0(i,j,k) + 3*phi_0(i,k,k-1));
	      }
	    }
		
	    aE (i,j,k) = dyz_dx - CE;
	    aW (i,j,k) = dyz_dx + CW;
	    aN (i,j,k) = dxz_dy - CN;
	    aS (i,j,k) = dxz_dy + CS;
	    aF (i,j,k) = dxy_dz - CF;
	    aB (i,j,k) = dxy_dz + CB;
	    aP (i,j,k) = aE (i,j,k) + aW (i,j,k) + aN (i,j,k) + aS (i,j,k) +
	      aF (i,j,k) + aB (i,j,k) + dxyz_dt
	      + (ce - cw) + (cn - cs) + (cf - cb);

	    sp (i,j,k) = v(i,j,k) * dxyz_dt - 
	      ( p(i,j+1,k) - p(i,j,k) ) * dxz +
	      RaGaVol * ( T(i,j,k) + T(i,j+1,k) )
	      - (cep + cem - cwp - cwm + 
		 cnp + cnm - csp - csm +
		 cfp + cfm - cbp - cbm);	    
	  }
    calc_dv_3D();
    applyBoundaryConditions3D();   
    return 0;
}

} // Tuna namespace















